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"Open windows, closing doors,
God can't help us anymore!
Souls forever, come and go,
Burn all the bridges and fire in the hole!"
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I think that means you have two weeks to claim it. Like how Xbox Live Games with Gold works. While the promotion is running, if you claim the game, it's yours. Afterwards you still pay full price.

The point is to get a lot of people playing the games, and then after the promotion, their friends see them playing it / see it in their library and go buy it (also it gets recommended if it's a great game).

This means stores fragmentation for PC platform, i.e. if the game is owned on Epic Games, but not owned on Steam even though the accounts are linked (you can link accounts via friend search, then it appears on the Epic account settings page), there isn't a reason to pay again if you want to install through the other store if owned on the first, as the platform is the same (PC).